Thomas F. Gilliss

2013

We demonstrate theoretical and experimental techniques for manipulating the
transverse spatial photonic degrees of freedom. Exploration of three interfero-
metric systems, including a single beam-splitter and two distinct setups of the
Mach-Zehnder type, reveals conditions necessary for observing Hong-Ou-Mandel
interference between two photons, each in an arbitrary linear superposition of
the two rst-order Hermite-Gaussian modes. For a Mach-Zehnder interferom-
eter arranged to discriminate between modes of odd and even one-dimensional
parity, we predict that if both input photons are in a balanced, in-phase su-
perposition of the rst-order modes, the resulting interference will alter the
transverse wavefunctions of the photons to be of Laguerre-Gaussian form. For
a balanced Mach-Zehnder interferometer, we nd that HOMI can be observed
for input photons in distinguishable transverse spatial modes. We experimen-
tally test the one-dimensional parity-based Mach-Zehnder for inputs of classical
coherent laser beams and nd that perfect constructive and destructive inter-
ference, at either output port, occurs under HOMI conditions. In addition, we
demonstrate the ability of this interferometer to sort inputs of arbitrary spatial
modes into their odd and even constituent modes.